On solving nonlinear transient heat transfer problems with random parameters

Computer Methods in Applied Mechanics and Engineering

Volumn 151, Issue 3-4, 1998, Pages 287-299

  Hien, Tran Duong ^a   Kleiber, Michał ^b  

^a WEST POMERANIAN UNIVERSITY OF TECHNOLOGY   (Poland)

^b INSTITUTE OF FUNDAMENTAL TECHNOLOGICAL RESEARCH   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE ELEMENT METHOD; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PERTURBATION TECHNIQUES; PROBABILITY; PROBLEM SOLVING; TEMPERATURE; VARIATIONAL TECHNIQUES;

HIERARCHICAL EQUATIONS; MEAN BASED SECOND MOMENT ANALYSIS; NONLINEAR TRANSIENT HEAT TRANSFER; RANDOM PARAMETERS; RANDOM TEMPERATURE FIELD; SECOND ORDER PERTURBATION;

HEAT TRANSFER;

EID: 0031647529     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(97)00152-7     Document Type: Article

References (21)

1. O.C. Zienkiewicz and Y.K. Cheung, Finite elements in the solution of field problems, The Engineer 220 (1965) 507-510.
2. J.T. Oden, Finite Elements of Nonlinear Continua (McGraw-Hill, 1972).
3. H.C. Martin, Finite element analysis of fluid flow, Proc. 2nd Conf. Matrix Meth. Struct. Mech., Dayton, Ohio, 1968.
4. J. Heuser, Finite element method for thermal analysis, NASA Tech. Note, TN D-7274, Goddard Space Flight Center, Greenbelt, 1972.
5. K.H. Huebner, Finite Element Method for Engineers (Wiley, 1975).
6. O.C. Zienkiewicz and R.L. Taylor, The Finite Element Method, 4th edition, Vol. 2 (McGraw-Hill, 1991).
7. M. Kleiber and Cz. Woźniak, Nonlinear Mechanics of Structures (PWN/Kluwer, 1991).
8. D.W. Pepper and J.C. Heinrich, The Finite Element Method. Series in Computational and Physical Processes in Mechanics and Thermal Sciences (Hemisphere, 1992).
9. C.S. Krishnamoorthy, Finite Element Analysis, 2nd edition (McGraw-Hill, 1994).
10. K.-J. Bathe, Finite Element Procedures (Prentice Hall, Englewood Cliffs, NJ, 1996).
11. T. Hisada and S. Nakagiri, Stochastic finite element method developed for structural safety and reliability, Proc. 3rd Int. Conf. on Struct. Safety and Reliability (1981) 395-402.
12. E.H. Vanmarcke and M. Grigoriu, Stochastic finite element analysis of simple beams, J. Engrg. Mech., ASCE 109(5) (1983) 1203-1214.
13. W.K. Liu, T. Belytschko and A. Mani, Random field finite elements, Int. J. Numer. Methods Engrg. 23 (1986) 1831-1845.
14. K.D. Tocher, The Art of Simulation (McGraw-Hill, 1968).
15. W.K. Liu, T. Belytschko and G.H. Besterfield, A variational principle for probabilistic mechanics, in: T.J.R. Hughes and E. Hinton, eds., Finite Element Method for Plate and Shell Structures. Vol. 2: Formulations and Algorithms (Pineridge Press, 1986) 285-311.
16. W.K. Liu, G.H. Besterfield and T. Belytschko, Variational approach to probabilistic finite elements, Engrg. Mech. 114(12) (1988) 2115-2133.
17. M. Kleiber and T.D. Hien, The Stochastic Finite Element Method (Wiley, 1992).
18. T.D. Hien and M. Kleiber, Finite element analysis based on stochastic Hamilton variational principle, Comput. Struct. 37(6) (1990) 893-902.
19. T.D. Hien and M. Kleiber, Stochastic finite element modelling in linear transient heat transfer, Comput. Methods Appl. Mech. Engrg. (1996).
20. M. Kleiber, Parameter Sensitivity in Nonlinear Mechanics (Wiley, 1997).
21. H.S. Carslaw and J.C. Jeager, Conduction of Heat in Solids (Oxford Univ. Press, 1959).